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Proof step 30 from proof pathex-put-cyclic (previous step)

st[r0 -- _type] .type = mkclasstype(class0), validrefs(str, (r ' + refs0) + r0 ', st[r -- _type] .type, st), st[r -- _type] .type ≤ ty, mkfs(class, ty, fieldvar) ' ∈ instfields(class0) ⊦ _type = mkfs(class, ty, fieldvar) ', r = r0, r0 = jvmref, r = jvmref, validrefs(str, r0 ' + (r ' + refs0) + r0 ', mkclasstype(class0), st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]), r ∈ refs0, dups(refs0), r0 ∈ refs0, is_obj(str, r0, st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]), ∃ refs. dups(refs) ∧ refs .first = r0 ∧ validrefs(str, refs, st[refs .first -- _type] .type, st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ ¬ validrefs(str, refs0, st[refs0 .first -- _type] .type, st) ∧ refs0 ≠ [] → ¬ validrefs(str, refs + refs0, ty, st)
Proof step 29:
¬ (¬ validrefs(str, r0 ', st[r0 ' .first -- _type] .type, st) ∧ r0 ' ≠ []), st[r0 -- _type] .type = mkclasstype(class0), validrefs(str, (r ' + refs0) + r0 ', st[r -- _type] .type, st), st[r -- _type] .type ≤ ty, mkfs(class, ty, fieldvar) ' ∈ instfields(class0) ⊦ _type = mkfs(class, ty, fieldvar) ', r = r0, r0 = jvmref, r = jvmref, validrefs(str, r0 ' + (r ' + refs0) + r0 ', mkclasstype(class0), st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]), r ∈ refs0, dups(refs0), r0 ∈ refs0, is_obj(str, r0, st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]), ∃ refs. dups(refs) ∧ refs .first = r0 ∧ validrefs(str, refs, st[refs .first -- _type] .type, st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)])

Rule argument

[crewrite-arg: validrefs-postfix , F , [st, ty, refs0, refs, str] → [st, st[r -- _type] .type, r0 ', r ' + refs0, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, st[r -- _type] .type, r0 ', r ' + refs0, str)]]